Formation damage simulator Development

In spite of many experimental studies of the formation damage of oil and gas bearing formations, there have been only a few reported attempts
to mathematically model the relevant processes and develop formation damage simulators (Civan, 1990, 1992, 1994, 1996). The use of these models in actual reservoir analysis and management has been rather limited because of the difficulties in understanding and implementing these models, as well as due to the limitations in the applicability of these models. Most present formation damage models consider a single fluid phase and the dominant formation damage mechanism is assumed to be the mobilization, migration, and retention of fine particles in porous matrix. Although, these models have been validated using experimental data obtained from reservoir core samples under controlled laboratory conditions, their applicability is rather limited in the field conditions. Most formation damage cases encountered in actual reservoirs are associated with multiphase flow and other factors which are not considered in the present single phase formation damage models. In addition, determination of the model parameters have not been well addressed.

Formation damage refers to permeability impairment by alteration of porous media due to rock-fluid and fluid-fluid interactions in geological porous formations. The phenomena leading to formation damage is a rather complicated process involving mechanical, physical, thermal, biological, and chemical factors. A formation damage model is a mathematical expression of the permeability impairment due to the alteration of the porous media texture and surface characteristics. This must be a dynamic model, which is coupled with a porous media fluid flow model to predict the mutual effects of formation damage and flow conditions in oil and gas reservoirs. Therefore, although the main emphasis and objective are to develop a formation damage model, we must also address the modeling of fluid flow in porous media. Thus, the basic constituents of the overall modeling effort involve:

1 porous media realization,

2 formation damage model,

3 fluid and species transport model,

4 numerical solution,

5 parameter estimation, and

6 model validation and application.

In reality, porous matrix and the fluids contained within pore volume display a discrete structure. For convenience, however, a continuum approach using average properties over representative elemental porous media volume is preferred. Porous media is considered in two parts:

1 the flowing phase, denoted by the subscript/, consisting of a suspension of fine particles flowing through and

2 the stationary phase, denoted by the subscript s, consisting of the porous matrix and the particles retained

Although it would be more rigorous to proceed through these steps, we resort to a continuum modeling approach using the average properties over representative elemental porous media for simplification purposes. The loss of information on the process details are then compensated by empirical formulations. Empiricism cannot be avoided because of the irregular structure of geological porous media and the disposition of various fluid phases and particulate matter.

Description of Fundamental Model Equations

The basic model equations are the mathematical expressions for the following (Civan, 1994):

Simulation of pressure; various species concentrations in the flowing fluid and the pore surface; porosity and permeability as functions of pore volume injected or time

Numerical Solution of Formation Damage Models

Depending on the level of sophistication of the considerations, theoretical approaches, mathematical formulations, and due applications, formation
damage models may be formed from algebraic and ordinary and partial differential equations, or a combination of such equations. Numerical
solutions are sought under certain conditions, defined by specific applications. The conditions of solution can be grouped into two classes:

1 initial conditions, defining the state of the system prior to any or further formation damage, and

2 boundary conditions, expressing the interactions of the system with its surrounding during formation damage.

Typically, boundary conditions are required at the surfaces of the system, through which fluids enter or leave, such as the injection and production
wells or ports, or that undergo surface processes, such as exchange or reaction processes. Algebraic formation damage models are either empirical correlations and/or obtained by analytical solution of differential equation models for certain simplified cases. Numerical solution methods for linear and nonlinear algebraic equations are well developed. Ordinary differential equation models describe processes in a single variable, such as either time or one space variable. However, as demonstrated in the following sections, in some special cases, special mathematical techniques can be used to transform multi-variable partial differential equations into single-variable ordinary differential equations. Amongst these special techniques are the methods of combination of variables and separation of variables, and the method of characteristics.

The numerical solution methods for ordinary differential equations are well developed. Partial differential equation models contain two or more independent variables. There are many numerical methods available for solution of partial differential equations, such as the finite difference method
(Thomas, 1982), finite element method (Burnett, 1987), finite analytic method (Civan, 1995), and the method of weighted sums (the quadrature
and cubature methods) (Civan, 1994, 1994, 1995, 1996, 1998; Malik and Civan, 1995; Escobar et al., 1997). In general, implementation of numerical methods for solution of partial differential equations is a challenging task.

In the following sections, several representative examples are presented for instructional purposes. They are intended to provide some insight into
the numerical solution process. Interested readers can resort to many excellent references available in the literature for details and sophisticated
methods. For most applications, however, the information presented in this chapter is sufficient and a good start for those interested in specializing
in the development of formation damage simulators. Although numerical simulators can be developed from scratch as demonstrated by the examples given in the following sections, we can save a lot of time and effort by taking advantage of ready-made softwares available from various sources. For this purpose, the spreadsheet programs are particularly convenient and popular. Various softwares for solving algebraic, ordinary, and partial differential equations are available. Commercially available reservoir simulators can be manipulated to simulate formation damage, such as by paraffin deposition as demonstrated by Ring et al. (1994).